Titlebook: Dynamics and Analysis of Alignment Models of Collective Behavior; Roman Shvydkoy Book 2021 Springer Nature Switzerland AG 2021 Cucker-Smal

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https://doi.org/10.1007/978-3-86226-841-2quation with a damping mechanism, while the latter is a degenerate fractional parabolic system with dissipation in the momentum equation. In this chapter we will go through the first routine but very much essential step—proving local existence of classical solutions and setting a convenient function

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https://doi.org/10.1007/978-3-86226-841-2The underlying theme will be to relate regularity and flocking behavior of the system to a new conserved quantity which is available in dimension 1 and for a few other exceptional multi-dimensional solutions. We highlight its analytical and physical roles in the alignment dynamics.

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https://doi.org/10.1007/978-3-86226-841-2 threshold condition is known, and in the singular case, the question is wide open. However, certain classes of special solutions do permit global existence. Those include solutions with small initial velocity fluctuations, small spectral gap of the symmetric velocity strain tensor, or special class

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Dynamics and Analysis of Alignment Models of Collective Behavior978-3-030-68147-0Series ISSN 2523-3343 Series E-ISSN 2523-3351

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https://doi.org/10.1007/978-3-86226-841-2The underlying theme will be to relate regularity and flocking behavior of the system to a new conserved quantity which is available in dimension 1 and for a few other exceptional multi-dimensional solutions. We highlight its analytical and physical roles in the alignment dynamics.

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Book 2021 system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems...Dynam

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2523-3343 ed. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems...Dynam978-3-030-68146-3978-3-030-68147-0Series ISSN 2523-3343 Series E-ISSN 2523-3351

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Dynamics and Analysis of Alignment Models of Collective Behavior